TSTP Solution File: ITP269_1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : ITP269_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:20:38 EDT 2024
% Result : Theorem 39.06s 6.83s
% Output : CNFRefutation 39.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 55
% Syntax : Number of formulae : 76 ( 28 unt; 47 typ; 0 def)
% Number of atoms : 30 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 21 ( 4 avg)
% Number of types : 13 ( 12 usr)
% Number of type conns : 23 ( 13 >; 10 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 22 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
nat: $tType ).
tff(decl_sort2,type,
num: $tType ).
tff(decl_sort3,type,
fun_nat_fun_nat_nat: $tType ).
tff(decl_sort4,type,
fun_nat_nat: $tType ).
tff(decl_sort5,type,
fun_nat_fun_nat_bool: $tType ).
tff(decl_sort6,type,
fun_nat_bool: $tType ).
tff(decl_sort7,type,
vEBT_VEBT: $tType ).
tff(decl_sort8,type,
bool: $tType ).
tff(decl_sort9,type,
option_nat: $tType ).
tff(decl_sort10,type,
list_VEBT_VEBT: $tType ).
tff(decl_sort11,type,
fun_num_nat: $tType ).
tff(decl_sort12,type,
fun_num_num: $tType ).
tff(decl_766,type,
bit_se2925701944663578781it_nat: fun_nat_fun_nat_nat ).
tff(decl_913,type,
one_one_nat: nat ).
tff(decl_919,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
tff(decl_929,type,
times_times_nat: fun_nat_fun_nat_nat ).
tff(decl_1008,type,
if_nat: bool > fun_nat_fun_nat_nat ).
tff(decl_1068,type,
list_u1324408373059187874T_VEBT: ( list_VEBT_VEBT * nat * vEBT_VEBT ) > list_VEBT_VEBT ).
tff(decl_1087,type,
nth_VEBT_VEBT: ( list_VEBT_VEBT * nat ) > vEBT_VEBT ).
tff(decl_1115,type,
suc: fun_nat_nat ).
tff(decl_1183,type,
bit0: fun_num_num ).
tff(decl_1185,type,
one: num ).
tff(decl_1193,type,
numeral_numeral_nat: fun_num_nat ).
tff(decl_1212,type,
the_nat: option_nat > nat ).
tff(decl_1232,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(decl_1248,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
tff(decl_1295,type,
power_power_nat: fun_nat_fun_nat_nat ).
tff(decl_1377,type,
divide_divide_nat: fun_nat_fun_nat_nat ).
tff(decl_1387,type,
modulo_modulo_nat: fun_nat_fun_nat_nat ).
tff(decl_1533,type,
vEBT_VEBT_high: fun_nat_fun_nat_nat ).
tff(decl_1535,type,
vEBT_VEBT_low: fun_nat_fun_nat_nat ).
tff(decl_1546,type,
vEBT_vebt_delete: ( vEBT_VEBT * nat ) > vEBT_VEBT ).
tff(decl_1567,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
tff(decl_1664,type,
aa_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(decl_1666,type,
aa_nat_nat: ( fun_nat_nat * nat ) > nat ).
tff(decl_1694,type,
aa_nat_fun_nat_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(decl_1696,type,
aa_nat_fun_nat_nat: ( fun_nat_fun_nat_nat * nat ) > fun_nat_nat ).
tff(decl_1719,type,
aa_num_nat: ( fun_num_nat * num ) > nat ).
tff(decl_1720,type,
aa_num_num: ( fun_num_num * num ) > num ).
tff(decl_1933,type,
fequal_nat: fun_nat_fun_nat_bool ).
tff(decl_1952,type,
pp: bool > $o ).
tff(decl_1953,type,
deg: nat ).
tff(decl_1954,type,
lx: nat ).
tff(decl_1956,type,
ma: nat ).
tff(decl_1958,type,
na: nat ).
tff(decl_1960,type,
summin: nat ).
tff(decl_1961,type,
treeList: list_VEBT_VEBT ).
tff(fact_3387_low__def,axiom,
! [X1: nat,X5: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X5) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3387_low__def) ).
tff(conj_0,conjecture,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(fact_5266_take__bit__eq__mod,axiom,
! [X5: nat,X3: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X5),X3) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X3),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5266_take__bit__eq__mod) ).
tff(fact_561_Suc__1,axiom,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_Suc__1) ).
tff(fact_1125_add_Ocommute,axiom,
! [X3: nat,X4: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X3),X4) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_add_Ocommute) ).
tff(fact_1101_mult_Ocommute,axiom,
! [X3: nat,X4: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X3),X4) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_mult_Ocommute) ).
tff(fact_16_hprolist,axiom,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_hprolist) ).
tff(fact_21__C114_C,axiom,
( pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg)))
& pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_eq_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__C114_C) ).
tff(c_0_8,plain,
! [X20261: nat,X20262: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X20261),X20262) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X20261),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X20262)) ),
inference(variable_rename,[status(thm)],[fact_3387_low__def]) ).
tff(c_0_9,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
tff(c_0_10,plain,
! [X27585: nat,X27586: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X27585),X27586) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X27586),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X27585)) ),
inference(variable_rename,[status(thm)],[fact_5266_take__bit__eq__mod]) ).
tcf(c_0_11,plain,
! [X1: nat,X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,plain,
aa_nat_nat(suc,one_one_nat) = aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)),
inference(split_conjunct,[status(thm)],[fact_561_Suc__1]) ).
tff(c_0_13,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(fof_nnf,[status(thm)],[c_0_9]) ).
tff(c_0_14,plain,
! [X19958: nat,X19959: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X19958),X19959) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X19959),X19958) ),
inference(variable_rename,[status(thm)],[fact_1125_add_Ocommute]) ).
tff(c_0_15,plain,
! [X19604: nat,X19605: nat] : ( aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X19604),X19605) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X19605),X19604) ),
inference(variable_rename,[status(thm)],[fact_1101_mult_Ocommute]) ).
tcf(c_0_16,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X2),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_17,plain,
! [X1: nat,X2: nat] : aa_nat_nat(aa_nat_fun_nat_nat(modulo_modulo_nat,X1),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),X2)) = aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
tcf(c_0_18,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_19,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_20,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_21,plain,
! [X2: nat,X1: nat] : aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,X1),X2) = aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_12]),c_0_17]) ).
tcf(c_0_22,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),
inference(split_conjunct,[status(thm)],[fact_16_hprolist]) ).
tcf(c_0_23,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_12]),c_0_20]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_21]),c_0_12]),c_0_19]),c_0_12]) ).
tcf(c_0_24,plain,
nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)) = vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_21]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_21]) ).
tcf(c_0_25,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one)))))),the_nat(vEBT_vebt_maxt(nth_VEBT_VEBT(list_u1324408373059187874T_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na),vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_low,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),na))),lx)),na)))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_num_nat(numeral_numeral_nat,aa_num_num(bit0,one))),deg))),
inference(split_conjunct,[status(thm)],[fact_21__C114_C]) ).
tcf(c_0_26,negated_conjecture,
~ pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))))))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
tcf(c_0_27,plain,
pp(aa_nat_bool(aa_nat_fun_nat_bool(ord_less_nat,aa_nat_nat(aa_nat_fun_nat_nat(if_nat(aa_nat_bool(aa_nat_fun_nat_bool(fequal_nat,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),aa_nat_nat(aa_nat_fun_nat_nat(divide_divide_nat,deg),aa_nat_nat(suc,one_one_nat)))),aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na))),the_nat(vEBT_vebt_maxt(vEBT_vebt_delete(nth_VEBT_VEBT(treeList,aa_nat_nat(aa_nat_fun_nat_nat(vEBT_VEBT_high,aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na)))),na)),aa_nat_nat(aa_nat_fun_nat_nat(bit_se2925701944663578781it_nat,na),aa_nat_nat(aa_nat_fun_nat_nat(plus_plus_nat,lx),aa_nat_nat(aa_nat_fun_nat_nat(times_times_nat,summin),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),na))))))))),ma)),aa_nat_nat(aa_nat_fun_nat_nat(power_power_nat,aa_nat_nat(suc,one_one_nat)),deg))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_12]),c_0_20]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_12]),c_0_19]),c_0_21]),c_0_12]),c_0_19]),c_0_24]),c_0_12]) ).
cnf(c_0_28,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_26,c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : ITP269_1 : TPTP v8.2.0. Released v8.0.0.
% 0.04/0.16 % Command : run_E %s %d THM
% 0.16/0.37 % Computer : n018.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 18:30:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.24/0.53 Running first-order model finding
% 0.24/0.53 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.06/6.83 # Version: 3.1.0
% 39.06/6.83 # Preprocessing class: FMLLSMLLSSSNFFN.
% 39.06/6.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.06/6.83 # Starting new_bool_3 with 900s (3) cores
% 39.06/6.83 # Starting new_bool_1 with 900s (3) cores
% 39.06/6.83 # Starting sh5l with 300s (1) cores
% 39.06/6.83 # Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 300s (1) cores
% 39.06/6.83 # new_bool_3 with pid 19712 completed with status 0
% 39.06/6.83 # Result found by new_bool_3
% 39.06/6.83 # Preprocessing class: FMLLSMLLSSSNFFN.
% 39.06/6.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.06/6.83 # Starting new_bool_3 with 900s (3) cores
% 39.06/6.83 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 39.06/6.83 # Search class: FGHSM-SMLM32-DFFFFFNN
% 39.06/6.83 # Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 39.06/6.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 39.06/6.83 # Starting new_bool_3 with 90s (1) cores
% 39.06/6.83 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 39.06/6.83 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 19721 completed with status 0
% 39.06/6.83 # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 39.06/6.83 # Preprocessing class: FMLLSMLLSSSNFFN.
% 39.06/6.83 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 39.06/6.83 # Starting new_bool_3 with 900s (3) cores
% 39.06/6.83 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 39.06/6.83 # Search class: FGHSM-SMLM32-DFFFFFNN
% 39.06/6.83 # Scheduled 13 strats onto 3 cores with 899 seconds (899 total)
% 39.06/6.83 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y with 68s (1) cores
% 39.06/6.83 # Starting new_bool_3 with 90s (1) cores
% 39.06/6.83 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 68s (1) cores
% 39.06/6.83 # Preprocessing time : 0.144 s
% 39.06/6.83 # SatCheck found unsatisfiable ground set
% 39.06/6.83
% 39.06/6.83 # Proof found!
% 39.06/6.83 # SZS status Theorem
% 39.06/6.83 # SZS output start CNFRefutation
% See solution above
% 39.06/6.83 # Parsed axioms : 13357
% 39.06/6.83 # Removed by relevancy pruning/SinE : 9203
% 39.06/6.83 # Initial clauses : 10232
% 39.06/6.83 # Removed in clause preprocessing : 1965
% 39.06/6.83 # Initial clauses in saturation : 8267
% 39.06/6.83 # Processed clauses : 6791
% 39.06/6.83 # ...of these trivial : 399
% 39.06/6.83 # ...subsumed : 1392
% 39.06/6.83 # ...remaining for further processing : 5000
% 39.06/6.83 # Other redundant clauses eliminated : 1751
% 39.06/6.83 # Clauses deleted for lack of memory : 0
% 39.06/6.83 # Backward-subsumed : 52
% 39.06/6.83 # Backward-rewritten : 84
% 39.06/6.83 # Generated clauses : 162642
% 39.06/6.83 # ...of the previous two non-redundant : 148287
% 39.06/6.83 # ...aggressively subsumed : 0
% 39.06/6.83 # Contextual simplify-reflections : 23
% 39.06/6.83 # Paramodulations : 160822
% 39.06/6.83 # Factorizations : 40
% 39.06/6.83 # NegExts : 0
% 39.06/6.83 # Equation resolutions : 1835
% 39.06/6.83 # Disequality decompositions : 0
% 39.06/6.83 # Total rewrite steps : 50754
% 39.06/6.83 # ...of those cached : 41568
% 39.06/6.83 # Propositional unsat checks : 1
% 39.06/6.83 # Propositional check models : 0
% 39.06/6.83 # Propositional check unsatisfiable : 1
% 39.06/6.83 # Propositional clauses : 153874
% 39.06/6.83 # Propositional clauses after purity: 64522
% 39.06/6.83 # Propositional unsat core size : 2
% 39.06/6.83 # Propositional preprocessing time : 0.000
% 39.06/6.83 # Propositional encoding time : 0.404
% 39.06/6.83 # Propositional solver time : 0.034
% 39.06/6.83 # Success case prop preproc time : 0.000
% 39.06/6.83 # Success case prop encoding time : 0.404
% 39.06/6.83 # Success case prop solver time : 0.034
% 39.06/6.83 # Current number of processed clauses : 4111
% 39.06/6.83 # Positive orientable unit clauses : 752
% 39.06/6.83 # Positive unorientable unit clauses: 63
% 39.06/6.83 # Negative unit clauses : 135
% 39.06/6.83 # Non-unit-clauses : 3161
% 39.06/6.83 # Current number of unprocessed clauses: 149763
% 39.06/6.83 # ...number of literals in the above : 473806
% 39.06/6.83 # Current number of archived formulas : 0
% 39.06/6.83 # Current number of archived clauses : 136
% 39.06/6.83 # Clause-clause subsumption calls (NU) : 1724561
% 39.06/6.83 # Rec. Clause-clause subsumption calls : 839763
% 39.06/6.83 # Non-unit clause-clause subsumptions : 1334
% 39.06/6.83 # Unit Clause-clause subsumption calls : 30622
% 39.06/6.83 # Rewrite failures with RHS unbound : 0
% 39.06/6.83 # BW rewrite match attempts : 8218
% 39.06/6.83 # BW rewrite match successes : 401
% 39.06/6.83 # Condensation attempts : 0
% 39.06/6.83 # Condensation successes : 0
% 39.06/6.83 # Termbank termtop insertions : 7615640
% 39.06/6.83 # Search garbage collected termcells : 203008
% 39.06/6.83
% 39.06/6.83 # -------------------------------------------------
% 39.06/6.83 # User time : 5.067 s
% 39.06/6.83 # System time : 0.239 s
% 39.06/6.83 # Total time : 5.306 s
% 39.06/6.83 # Maximum resident set size: 54688 pages
% 39.06/6.83
% 39.06/6.83 # -------------------------------------------------
% 39.06/6.83 # User time : 14.126 s
% 39.06/6.83 # System time : 0.374 s
% 39.06/6.83 # Total time : 14.501 s
% 39.06/6.83 # Maximum resident set size: 29972 pages
% 39.06/6.83 % E---3.1 exiting
%------------------------------------------------------------------------------